• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.3
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• pp.225-240
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• 2006

In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.

• Bulletin of the Society of Naval Architects of Korea
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• v.14 no.1
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• pp.1-10
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• 1977

The major objects of this report are to supplement data of natural frequencies of thin elastic rectangular plates to the available data, and to give an experimental verification for natural frequencies obtained by Rayleigh-Ritz method, the generation set of which are eigenfunctions of Euler beams. For the first object the following five models, for which data only for the fundamental mode or data only for square plates are available, are adopted; (1) two opposed edges are clamped and the other two opposed edges simply supported (C-C, S-S), (2) one edge is simply supported and the other three edges clamped (C-C, C-S), (3) one edge is free and the other three edges clamped (C-C, C-F), (4) two adjacent edges are clamped and the other two adjacent edges free (C-F, C-F). For the (C-C, S-S) model the frequency equation obtained with the mode shapes assumed as of a single trigonometric series is solved. And for the other four models Rayleigh-Ritz method taking eigenfunctions of Euler beams as the generating set is applied. The numerical examples are obtained up to the fourth, the fifth or the sixth order depending on the range of the aspect ratio (0.1-10.0). The number of terms in the generating set for Rayleigh-Ritz method is fifteen for all models. For the experiment three models made of 3.2mm thickness mild steel plate for general structure use were prepared in following size; $300mm{\times}600mm,\;600mm{\times}600mm\;and\;900mm{\times}600mm$. Their boundary conditions are made to fit (C-C, C-F) condition. From the experiment mechanical impedance curves based on the frequency response method were obtained together with phase relation diagrams. The experimental data are resulted in good conformity to calculated values.

• Magazine of the Korean Society of Agricultural Engineers
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• v.28 no.4
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• pp.49-56
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• 1986

This study was carried out to investigate mechanical characteristics of the uniformly loaded skew-plate at 4 kinds of boundary condition : i) all edges are clamped (BC-1) , ii) all edges are simply supported (BC- 2), iii) two opposite edges are clamped and the other two edges are free (BC-3), and iv )two opposite edges are simply supported and the other two edges are free (BC-4). Various skew angles, 0$^{\circ}$, 10$^{\circ}$, 15$^{\circ}$, 30$^{\circ}$, 40: 45: and 60, of the plate were tested for the above boundary conditions. Resutts obtained from the study are summarized as follows ; 1.The lateral displacement at the center of a skew- plate was decreased as the skewangle increased at all of the boundary conditions. The decrements of the conditions of BC-3 and BC-4 were considerable. And, difference of the displacement between the boundary conditions was decreased as the skew-angle was increased. 2. X-moments (to the Y-axis) at the center of a skew- plate and the minimum principal moments were shown as a similar pattern of change with respect to the skew-angle variation between BC-i and BC-2 and between BC-3 and BC-4, and the pattern of change at the conditions of BC-3 and BC-4 were shown higher rates than those for the conditions of BC-i and BC-2 3.Y-moments (to the X- axis) at the center of a skew-plate and the maximum principal moment were decreased as the skew-angle increased in a similar pattern at all of the boundary conditions. 4.X-moments at the obtuse angle side of a skew-plate were shown as a parabolic pattern of change (frist increased after then decreased) as the skew-angle increased, and a skew-angle resulting the maximum absolute moment was depended on the boundary conditions. 5.Y-moments at the obtuse angle side of a skew-plate were affected by the skewangle much more at the boundary condtions of BC-2 and BC-4 than at the conditions of BC-i and BC-3. 6.Maximum principal moments at the obtuse angle side of a skew-plate at the skew angle of 40$^{\circ}$- 45$^{\circ}$ were resulted almost the same value at all of the boundary conditions .

• Bulletin of the Society of Naval Architects of Korea
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• v.15 no.2
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• pp.1-11
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• 1978

Using the elliptical cylindrical function, the added masses of thin rectangular plates vibrating elastically in an infinite ideal fluid are calculated. For the boundary conditions of the plates, two models are adopted. The plate which is simply-supported on two opposite edges while the other edges are clamped is one and the other is the plate which is simply-supported on two opposite edges while the other edges are free. Same examples are calculated numerically for the fundamental mode in each cases. And the effect of the boundary condition on the added mass are investigated by comparing these data with those of Kim's[4] which were calculated for the simply-supported plates by the same method. It is concluded that it is possible to predict the added mass of a rectangular plate, whose boundary condition is not treated in this report, by using the result of this investigation.

• Journal of Korean Association for Spatial Structures
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• v.6 no.4 s.22
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• pp.81-92
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• 2006

This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.184.2-184.2
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• 2005

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.11
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• pp.943-950
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• 2013

This paper discusses a harmonic response estimation method on the L$\acute{e}$vy plate with two opposite edges simply supported and the other two edges having free boundary conditions. Since the equation of motion of the plate is not self-adjoint, the modes are not orthogonal to each other on the domain. Noting that the L$\acute{e}$vy plate can be expressed using one term sinusoidal function that is orthogonal to other sinusoidal functions, this paper suggested the calculation method that is equivalent to finding a least square error minimization solution of the finite number of algebraic equations. Example problems subjected to a distributed area loading and a distributed line loading are defined and their solutions are provided. The solutions are compared to those of the commercial code, ANSYS. According to the verification results, it is expected that the suggested method will be useful to predict the forced response on the L$\acute{e}$vy plate with the distributed area or line loading conditions.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.89-95
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• 2014

We analyze the buckling of a thin elastic plate due to intrinsic stresses in thin films attached to the surfaces of the plate. In the case of cylindrical buckling, it is shown that for a plate with clamped edges compressive intrinsic film stresses can cause flexural buckling of the plate, while tensile intrinsic film stresses cannot. For a plate with free edges, film intrinsic stresses, compressive or tensile, cannot cause buckling.

• Journal of KSNVE
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• v.4 no.3
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• pp.283-295
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• 1994

This work presents the experimental and finite element analysis results for the free vibration of 4 edges clamped, isotropic square plates with 2 collinear circular holes. Natural frequencies of finite element analysis are obtained for the complete square plate, the square plates with a central circular hole and the square plates with 2 collinear circulare holes. And natural frequencies are experimentally measured for the complete square plate, the square plate with a central circular hole(d = 150 mm) and the square plates with 2 collinear circular holes. Agreement between experimental and FEM results is excellent. Mode shapes in special case are presented. The conclusions of the study are as follows. There is little variation of nondimensional frequency parameters for the first six mode when the aspect ratio of circular hole is less than 1/6 in the isotropic square plates with 2 collinear circular holes. And the first nondimensional frequency parameter doesn't vary as the aspect ratio of circular hole increase.

• Structural Engineering and Mechanics
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• v.5 no.1
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• pp.85-104
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• 1997

The paper investigates the influence of lateral restraint on the buckling behaviour of plate under non-uniform compression. The unloaded edges are assumed to be partially restrained against translation in the plane of the plate and the distributions of the resulting forces acting on the plate are shown. The stability analysis is done numerically using the Galerkin method and various strategies the economize the numerical implementation are presented. Results are obtained showing the variation of the buckling load, from free edge translation to fully restrained, with unloaded edges simply supported, clamped and partially restrained against rotation for various plate aspect ratios and stress gradient coefficients. An apparent decrease in the buckling load is observed due to these destabilizing forces acting in the plate and changes in the buckling modes are observed by increasing the intensity of the lateral restraint. A comparison is made between the budding loads predicted from various formulas in stability standards based on free edge translation and the values derived from the present investigation. A difference of about 34% in the predicted buckling load and different buckling mode were found.